<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:msub> <a:mrow> <a:mi>L</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msub> </a:math> Adaptive Fractional Control Optimized by Genetic Algorithms with Application to Polyarticulated Robotic Systems

Abstract

Recently, an adaptive control approach has been proposed. This approach, named <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M2"> <a:msub> <a:mrow> <a:mi>L</a:mi> </a:mrow> <a:mrow> <a:mn>1</a:mn> </a:mrow> </a:msub> </a:math> adaptive control, involves the insertion of a low-pass filter at the input of the Model Reference Adaptive Control (MRAC). This controller has been designed to overcome several limitations of classical adaptive controllers such as (i) the initialization of estimated parameters, (ii) the stability problems with high adaptation gains, and (iii) the appropriate parameter excitation. In this paper, a new design of the filter is presented, used for <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M3"> <c:msub> <c:mrow> <c:mi>L</c:mi> </c:mrow> <c:mrow> <c:mn>1</c:mn> </c:mrow> </c:msub> </c:math> adaptive control, for which the desired performances are guaranteed (appropriate values of the control during start-up, a high filtering of noises, a reduced time lag, and a reduced energy consumption). Parameters of the new proposed filter have been optimised by genetic algorithms. The proposed <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" id="M4"> <e:msub> <e:mrow> <e:mi>L</e:mi> </e:mrow> <e:mrow> <e:mn>1</e:mn> </e:mrow> </e:msub> </e:math> adaptive fractional control is applied to a polyarticulated robotic system. Simulation results show the efficiency of the proposed control approach with respect to the classical <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" id="M5"> <g:msub> <g:mrow> <g:mi>L</g:mi> </g:mrow> <g:mrow> <g:mn>1</g:mn> </g:mrow> </g:msub> </g:math> adaptive control in the nominal case and in the presence of a multiplicative noise.